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Month: September 2012

Yesterday, Mardy Fish withdrew from his fourth-round match against Roger Federer. As we saw earlier today, Federer may gain some benefit from the extra rest, but with the additional rest days built into the grand slam schedule, Roger runs the risk of getting too little time on court.

What’s the true effect, then? Will the extra rest make Federer an even bigger favorite in his quarterfinal match against Tomas Berdych? Or will match-court rust hold him back?

As it turns out, there is virtually no effect. Players handed a walkover win almost exactly half of their next matches, and a closer look at those matches reveals that 50% is about what we would’ve expected from them, walkover or not.

To hunt for a potential relationship, I found 139 ATP main draw walkovers since 2001 where the winner went on to play another match at the same tournament–in other words, excluding finals. While it may seem that players tend to withdraw when they’re least likely to win a match (as with Fish this week, or like the other two players to withdraw before facing Federer this year), there’s nothing to that theory, either. The average pre-match odds of the withdrawing player are about 51%.

Thus, we can work on the assumption that there’s little bias in the pool of 139 men who received a free pass to the next round. For every Federer, there’s a Donald Young advancing uncontested over Richard Gasquet. Balancing the withdrawals of players without a chance may be higher-ranked players who are quicker to withdraw because their success allows them to play it safe and make longer-term decisions.

In the 139 follow-up matches, our players went 67-72, winning 48.2% of the time. Prematch predictions (generated by Jrank) would have projected a winning percentage of 48.9%.

If we narrow the search to slams, we get a nearly-meaningless pool of only 12 matches. The player coming off the walkover went 6-6; prematch numbers would’ve predicted 7-5. Perhaps rust does play a small part; considerably more likely is that the walkover simply doesn’t affect the beneficiary.

For Federer fans, though, there’s little reason for concern. This is the ninth time in his career he’s advanced via walkover, and he’s only lost the next match twice. One of those was in 2002. The other was in Indian Wells in 2008. The man who beat Fed? Mardy Fish.

Before we get carried away, let’s find out what the numbers tell us. As we’ll see, slam champions usually are the men who spent fewer minutes on court getting to the final. It’s less clear, though, whether there is a causal link: After all, a better player should have an easier time of it in the early going.

The ATP has complete match-length numbers for our purposes going back to 2001. That gives us enough data to look at the last 47 slams.

In the last 47 grand slam finals, the favorite (defined simply as the guy with the better ATP ranking) won 33 times. In 6 of the 14 slam finals in which the underdog won, the underdog had spent less time on court in his previous six matches than the favorite did in his. Pretty good, huh?

One problem: Six other times, the favorite won the final despite having spent more time on court. So if you have to pick between the favorite and the better-rested player, there’s nothing in this sample to differentiate your choices.

A more positive takeaway occurs when the favorite has spent less time on court. There have been 35 such finals since 2001, and the better-rested favorite has gone 27-8. Most of the time, the favorite has reached the final expending less effort than his challenger did, and perhaps we can view that as a confirmation of his status as favorite.

(If you prefer games played to minutes on court, perhaps in deference to the Nadal and Djokovic speed of play, rest assured the numbers come out almost identical. There are a few cases where players spent less time on court but played more games–or vice versa–but if the analysis above replaced minutes with games, the results would be the same.)

All else equal, we’d bet on the finalist who has spent less time on court. But that doesn’t necessary imply that the better-rested player is more likely to win the final because he hasn’t spent as much time on court. That seems particularly true at slams, where players almost always get a day of rest between matches, and where top contenders almost never play doubles.

More likely is that one player spent less time on court because he is the favorite. Surely no one was surprised when Federer breezed past Verdasco, and few were surprised that Murray needed more time to put away Feliciano Lopez. Time on court is a clue that one man is playing better tennis, regardless of whether the extra rest aids him in later matches.

We can probably all agree on a safer claim: All else equal, the world’s best would certainly prefer to spend less time on court, even if it doesn’t boost his odds of winning the final. It might be gratifying to fight off an early challenge, but surely it’s more enjoyable to remind the rest of the field why you’re the favorite.